If the main part of the mathematical processing of the part drawing is to calculate the size of the part processing track, that is, to calculate the coordinates of the base point and node of the part processing appearance, or the coordinates of the base point and node. Tool center appearance node, used to compile machining programs. Generally, CNC machine tools have only linear and circular interpolation performance. As for the plane appearance composed of straight lines and arcs, the key mission of numerical calculation during programming is to find the coordinates of each base point.
1. Meaning of base point
The intersection or tangent point of the differential geometric element lines that make up the appearance of the part is called the base point. The base point can be directly used as the starting point or end of its activity track.
2. Content of direct calculation
According to the requirements of filling in the processing program sheet, the contents of direct calculation of the base point include: the coordinates of the starting point and end of each moving track in the selected coordinate system, and the center coordinate value of the circular arc moving track.
The method of direct calculation of base point is relatively simple. It can usually be completed manually according to the known conditions given by the part drawing. That is, according to the size given in the part drawing, the value can be calculated directly by applying the relevant knowledge of algebra, trigonometry, geometry or analytical geometry. When calculating, pay attention to the number of digits after the decimal point and leave enough to ensure sufficient accuracy.
Calculation of node coordinates
As for the composition of some plane appearance right and wrong circle equation curves y = f (x), such as involute and Archimedes spiral, we can only approach them with Machinable straight lines and arcs. At this time, the mission of numerical calculation is to calculate the coordinates of nodes.
1. Definition of nodes
When the NC machine tool without non-circular curve interpolation performance is selected to process the parts with Non-circular Curve appearance, in the preparation of machining program, multiple straight lines or arcs are often used to approximately replace the non-circular curve, which is called fitting processing. The intersection or tangent point of the fitting line segment is called a node.
2. Calculation of node coordinates
The calculation of node coordinates is difficult and workload is large, so it is often completed by computer. If necessary, it can also be calculated manually. The commonly used methods are straight-line approach method (equal spacing method, equal step method, and equal deviation method) and circular arc approach method. Maxchange